Elliptic curve isogeny class with Cremona label 18240cg (LMFDB label 18240.bl)

• Label: 18240cg
• Number of curves: $2$
• Conductor: $18240$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 18240cg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 18240cg do not have complex multiplication.

Modular form 18240.2.a.cg

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 18240cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
18240.bl2	18240cg1	\([0, -1, 0, -5025, 482625]\)	\(-53540005609/350208000\)	\(-91804925952000\)	\([2]\)	\(64512\)	\(1.3627\)	\(\Gamma_0(N)\)-optimal
18240.bl1	18240cg2	\([0, -1, 0, -127905, 17612097]\)	\(882774443450089/2166000000\)	\(567803904000000\)	\([2]\)	\(129024\)	\(1.7092\)